KABUL -- U.S. special peace envoy Zalmay Khalilzad has held fresh talks with the Afghan leadership in Kabul, amid an uptick in violence that threatens to unravel a February peace deal between the United States and the Taliban.

After holding talks with Taliban representatives in Qatar, Khalilzad flew to Afghanistan on May 20, as the leader of the Taliban said the militants were committed to the deal with Washington despite stepping up violence against government forces since it was signed.

In Kabul, Khalilzad met with President Ashraf Ghani and Abdullah Abdullah, who is expected to lead the intra-Afghan peace talks with the Taliban, according to the Afghan presidency.

The sides discussed the importance of 'a cease-fire or reduction in violence before the start of direct talks,' a statement said.

Khalilzad's visit comes days after Ghani and Abdullah reached a power-sharing agreement under which Abdullah, his political rival, leads the High Peace Council.

A power struggle between Ghani and Abdullah, both of whom claimed to have won the presidential election in September, had been one of the main impediments to the start of intra-Afghan negotiations to end more than 18 years of war.

The talks were to begin on March 10 under the agreement between the Taliban and the United States, which calls for U.S. and foreign troops to withdraw from Afghanistan following an intra-Afghan deal and in exchange for security guarantees.

Khalilzad's visit also comes as at least 14 people were killed in attacks late on May 19 on two mosques in Afghanistan where worshippers were breaking their Ramadan fast.

The Taliban denied carrying out the killings, which came after last week's attack on a maternity hospital in Kabul in which 24 people, included newborns, were shot dead.

The Taliban also denied carrying out the maternity attack, which Washington said bore the hallmarks of the Islamic State (IS) militant group.

In a message that coincided with Khalilzad's visit to Kabul, the Taliban's reclusive leader, Haibatullah Akhundzada, called on Washington 'not to waste' the opportunity offered by the deal to end the United States' longest war.

In the message released ahead of next week's Eid al-Fitr holiday that marks the end of the Islamic month of Ramadan, Akhundzada urged U.S. officials to not afford anyone the opportunity to obstruct, delay, and ultimately derail this internationally recognized bilateral agreement.'

The Taliban has so far rejected repeated calls for a cease-fire by the Afghan government.

On May 19, at least 11 people were killed and 16 were wounded in one of the mosque attacks in Charekar, the capital of the central province of Parwan, security officials told RFE/RL.

'Unknown gunmen fired on people praying inside a mosque during iftar time,' said Wahida Shahkar, spokeswoman for the governor of Parwan, referring to the meal eaten to break daytime fasting during the Islamic holy month.

The Interior Ministry blamed the attack on the Taliban. The militants denied responsibility and said Afghan security forces were to blame.

The Parwan Province police chief, Haroon Mubariz Parwan, told RFE/RL that Islamic State militants were suspected of having carried out the attack.

Three other people were killed in a similar attack late on May 19 on a mosque in the southeastern Khost Province, Talib Mangal, a spokesman for the provincial governor, told RFE/RL.

Mangal said a child was also wounded in the attack in Khost's Sabari district.

No one claimed responsibility for the Khost attack.

In the northern Takhar Province, suspected Taliban militants attacked a checkpoint late on May 19, leaving nine dead, officials said.

Six others were wounded in the incident, which took place in the province's Khawja Bahauddin district.

Elsewhere on May 19, Afghan security forces clashed with Taliban fighters around the city of Kunduz, a strategically important center that the militants have briefly captured twice in recent years.

Security forces largely repelled the Taliban offensive with the help of air support.

Assadullah Khalid, acting defense minister, said during a visit to the city that more than 50 militants and eight security-force members had been killed.